Integrate e^2x / SQRT (e^2x + 3)

[donleo]

Homework Statement

Integrate e^2x / SQRT [(e^2x) + 3)]

Homework Equations

The Attempt at a Solution

i know the solution, is: SQRT [(e^2x) + 3]

but i have no idea why. Please I need help

thank you

 

[eok20]

Have you tried substitution?

 

[donleo]

Have you tried substitution?

yes, t=e^2x + 3 but still nothing

 

[eok20]

Ok, if t=e^2x + 3 then dt = 2e^2x, and what does the integral become in terms of t and dt?

 

[donleo]

Ok, if t=e^2x + 3 then dt = 2e^2x, and what does the integral become in terms of t and dt?

i have 1/2 (dt/ sqrt t)

so 1/2 t^(3/2) / (3/2)

then sqrt t / 3

then sqrt (e^2x+3)^3 / 3

its not the solution, it may be sqrt (e^2x+3)

 

[eok20]

Close, you have 1/2(dt/sqrt(t)) = 1/2 t^(-1/2) dt. You integrated 1/2 t^(1/2) dt instead

 

[Gib Z]

sqrt t is in the Denominator! So the power of t isn't 1/2, but actually... ?

 

[donleo]

Close, you have 1/2(dt/sqrt(t)) = 1/2 t^(-1/2) dt. You integrated 1/2 t^(1/2) dt instead

its true! lol, it was my mistake, i forgot the change t^1/2 -> t^-1/2

thank you!